Identifying changes in the reproduction number, rate of spread, and doubling time during the course of the COVID-19 outbreak whilst accounting for potential biases due to delays in case reporting both nationally and subnationally in Germany. These results are impacted by changes in testing effort, increases and decreases in testing effort will increase and decrease reproduction number estimates respectively (see Methods for further explanation).
Figure 1: The results of the latest reproduction number estimates (based on estimated cases with a date of infection on the 2020-03-22) in Germany, stratified by region, can be summarised by whether cases are likely increasing or decreasing. This represents the strength of the evidence that the reproduction number in each region is greater than or less than 1, respectively.
| Estimate | |
|---|---|
| New infections | 5764 (3253 – 8030) |
| Expected change in daily cases | Likely increasing |
| Effective reproduction no. | 1.2 (0.9 – 1.6) |
| Doubling time (days) | 18 (6.7 – Cases decreasing) |
| Adjusted R-squared | 0.54 (-0.072 – 0.98) |
Table 1: Latest estimates (as of the 2020-03-22) of the number of cases by date of infection, the expected change in daily cases, the effective reproduction number, the doubling time, and the adjusted R-squared of the exponential fit. The mean and 90% credible interval is shown for each numeric estimate.
Figure 2: A.) Cases by date of report (bars) and estimated cases by date of infection. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 90% credible interval. Estimates are shown until the 2020-03-22.Dark grey ribbon = 50% credible interval. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Figure 3: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Estimates are shown until the 2020-03-22. Light grey ribbon = 90% credible interval; dark grey ribbon = the 50% credible interval. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Figure 4: Cases with date of infection on the 2020-03-22 and the time-varying estimate of the effective reproduction number (bar = 90% credible interval). Regions are ordered by the number of expected daily cases and shaded based on the expected change in daily cases. The dotted line indicates the target value of 1 for the effective reproduction no. required for control and a single case required for elimination.
Figure 5: Time-varying estimate of the effective reproduction number (light grey ribbon = 90% credible interval; dark grey ribbon = 50% credible interval) in the regions expected to have the highest number of incident cases. Estimates are shown up to the 2020-03-22. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence. The dotted line indicates the target value of 1 for the effective reproduction no. required for control.
Figure 6: Cases by date of report (bars) and estimated cases by date of infection (light grey ribbon = 90% credible interval; dark grey ribbon = 50% credible interval) in the regions expected to have the highest number of incident cases. Estimates are shown up to the 2020-03-22.Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
Figure 7: Time-varying estimate of the effective reproduction number (light grey ribbon = 90% credible interval; dark grey ribbon = 50% credible interval) in all regions. Estimates are shown up to the 2020-03-22. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence. The dotted line indicates the target value of 1 for the effective reproduction no. required for control.
Figure 8: Cases by date of report (bars) and estimated cases by date of infection (light grey ribbon = 90% credible interval; dark grey ribbon = 50% credible interval) in all regions. Estimates are shown up to the 2020-03-22. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.
| Region | New infections | Expected change in daily cases | Effective reproduction no. | Doubling time (days) |
|---|---|---|---|---|
| Baden Wurttemberg | 1720 (641 – 2657) | Likely increasing | 1.3 (0.8 – 1.8) | 14 (4.9 – Cases decreasing) |
| Bavaria | 2005 (822 – 3064) | Likely increasing | 1.3 (0.8 – 1.8) | 14 (5.1 – Cases decreasing) |
| Berlin | 225 (80 – 339) | Unsure | 1.1 (0.7 – 1.5) | 29 (5.4 – Cases decreasing) |
| Brandenburg | 117 (41 – 184) | Likely increasing | 1.4 (0.8 – 1.9) | 11 (4.1 – Cases decreasing) |
| Bremen | 26 (1 – 44) | Unsure | 1.3 (0.6 – 1.9) | 18 (3.3 – Cases decreasing) |
| Hamburg | 181 (64 – 287) | Unsure | 1 (0.6 – 1.4) | -570 (8 – Cases decreasing) |
| Hesse | 318 (119 – 515) | Unsure | 1.2 (0.7 – 1.6) | 22 (5.6 – Cases decreasing) |
| Lower Saxony | 512 (200 – 782) | Likely increasing | 1.3 (0.8 – 1.7) | 12 (4.7 – Cases decreasing) |
| Mecklenburg Vorpommern | 47 (6 – 73) | Likely increasing | 1.5 (0.8 – 2.2) | 9 (3.1 – Cases decreasing) |
| North Rhine Westphalia | 1462 (621 – 2356) | Likely increasing | 1.3 (0.8 – 1.7) | 14 (4.9 – Cases decreasing) |
| Rhineland Palatinate | 322 (131 – 522) | Unsure | 1.3 (0.8 – 1.7) | 18 (5.5 – Cases decreasing) |
| Saarland | 161 (28 – 266) | Likely increasing | 1.7 (0.8 – 2.5) | 6.8 (2.9 – Cases decreasing) |
| Saxony | 231 (82 – 358) | Likely increasing | 1.3 (0.8 – 1.7) | 15 (5 – Cases decreasing) |
| Saxony Anhalt | 85 (25 – 140) | Likely increasing | 1.3 (0.8 – 1.8) | 14 (4.7 – Cases decreasing) |
| Schleswig Holstein | 125 (44 – 203) | Likely increasing | 1.3 (0.8 – 1.7) | 14 (4.6 – Cases decreasing) |
| Thuringia | 78 (33 – 131) | Unsure | 1.1 (0.7 – 1.5) | 160 (7.1 – Cases decreasing) |
Table 2: Latest estimates (as of the 2020-03-22) of the number of cases by date of infection, the effective reproduction number, and the doubling time in each region. The mean and 90% credible interval is shown.
Abbott, Sam, Joel Hellewell, James D. Munday, and Sebastian Funk. 2020. “NCoVUtils: Utility Functions for the 2019-Ncov Outbreak.” - - (-): –. https://doi.org/10.5281/zenodo.3635417.
Gehrcke, Jan-Philip. 2020. “COVID-19 Case Numbers in Germany by State, over Time.” Github Repository. Germany. https://github.com/jgehrcke/covid-19-germany-gae.
Xu, Bo, Bernardo Gutierrez, Sarah Hill, Samuel Scarpino, Alyssa Loskill, Jessie Wu, Kara Sewalk, et al. n.d. “Epidemiological Data from the nCoV-2019 Outbreak: Early Descriptions from Publicly Available Data.” http://virological.org/t/epidemiological-data-from-the-ncov-2019-outbreak-early-descriptions-from-publicly-available-data/337.